Advanced Topics in Network Science

1 Concepts: Graph Neural Networks

1.1 What to learn in this module

In this module, we will learn how to use neural networks to learn representations of graphs. We will learn: - Fourier transform on image - Fourier transform on graph - Spectral filters - Graph convolutional networks - Popular GNNs (GCN, GAT, GraphSAGE, and GIN)

1.2 Theoretical Exercises

Pen and paper exercises

• ✍️ Pen and paper exercises

The pen and paper exercises will help you understand the mathematical foundations of graph neural networks, including:

1. Spectral Graph Theory: Understanding eigenvalues and eigenvectors of graph matrices
2. Fourier Analysis on Graphs: Extending classical signal processing to graph domains
3. Convolution Operations: Defining convolution for irregular graph structures
4. Message Passing: Mathematical formulation of information aggregation in graphs
5. Network Architecture Design: Principles for designing effective GNN architectures

These exercises provide the theoretical foundation necessary to understand how graph neural networks process and learn from graph-structured data.